That really stumped me. So here's the elaboration that I found on nualeargais.ie: "one can choose to form this by a definite noun of the partitive dative with the preposition de + article ( in German there would be here rather the partitive genitive!). This is especially so if the first noun should remain indefinite:
e.g.: cuid den airgead = a share of the money("part of the money"), ceathrú den úll = quarter of the apple ("from the apple"), roinnt de na fir = some of the men ("share of the men")

The partitive dative ist always necessary, if both nouns are definite (also here one would use the genitive in German): mo chuid den airgead = my share of the money ("my part of the money")".

I think the clue here is that in Irish, the dative has another function from the standard one in Indo-European languages. "Sometimes the dative has functions unrelated to giving. In Scottish Gaelic and Irish, the term dative case is used in traditional grammars to refer to the prepositional case-marking of nouns following simple prepositions and the definite article. " (https://en.m.wikipedia.org/wiki/Dative_case)

"In Irish and Scottish Gaelic, nouns that are the objects of (most) prepositions may be marked with prepositional case, especially if preceded by the definite article. In traditional grammars, and in scholarly treatments of the early language, the term dative case is incorrectly used for the prepositional case. This case is exclusively associated with prepositions. " (https://en.m.wikipedia.org/wiki/Prepositional_case)

Yep, completely true, but I think there might also be a little bit more to it than that. There was an Irish language newspaper called Inniú and it meant 'Today'. I'm wondering if it was something unique to one of the dialects that was dropped.

According to Wikipedia, Inniú was founded in 1943, while the spelling reforms of the 1940s were still underway. Inniu is a reformed spelling, and it's possible that inniú represented an early attempt at a reformed spelling, and when the official reformed spellings were released, they decided not to rename the publication.

That's just a guess on my part - Dineen didn't have either inniu or inniiú in his dictionary.

What exactly does 'strong plural' mean?
I had understood it to mean simultaneously:
1. that npl. had a proper suffix, i.e. not only í(the) tagged on and
2. that gpl. would be identical to npl. (rather than ns.).

But now I see for
ns. leabharlann:
1. npl. leabharlanna and 2. gpl. leabharlann.
So does leabharlann have a 'strong plural'?